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Egg Heads Puzzle 


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Egg Heads Puzzle 

Written By: George Hart 


Band saw (1) 

Belt Sander (1) 

Copier (1) 

Drill (1) 

Heat gun (1) 
for toner transfer 

Scroll saw (1) 


• Hardwood (1) 

• Plastic (1) 
aka plexiglass 

• Wood Finish (1) 

• Templates (1) 

Copy and enlarge from photos or 
download the full-size PDF from the files 


As a retirement present for Joe Malkevitch, a geometer friend who likes puzzles, I designed 
and built this 1 '-diameter Egg Heads puzzle from Vi" walnut. 

Many of my sculpture and puzzle designs require laser-cutting or other computer-guided 
fabrication technology to accurately produce intricate parts. But this design is simple enough 
that you can make the parts yourself with ordinary shop tools such as a band saw and belt 

The ease of fabricating the parts doesn't imply ease of assembly, however. After cutting out 
the 30 parts, you'll find it requires all of your puzzle-solving skills to interweave and interlock 

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Egg Heads Puzzle 

them into a symmetric structure. Here are instructions for making and assembling your own 


• The template can be scaled up to be 1 1" long using a copier, or you can download the full- 
sized PDF version from the files section. The shape fits diagonally on a standard 8 1 /2"x1 1" 
sheet of paper. 

• I designed a simple egg-shaped head that's easy to saw, but you can personalize the face 
of yours if desired. However, don't modify the neck notch or the 90° notch at the back of 
the head, which are carefully positioned for proper assembly. 

You could just trace the paper 
outline, but a more accurate 
technique is to do a hot toner 
transfer. Either print the template 
with a laser printer or, if you use an 
inkjet printer, photocopy the printed 
template so you have a toner- 
based copy. 

Tape it, toner side down, to the 
acrylic and warm it with a heat gun 
as you rub the paper with the back 
of a spoon. Hot toner will melt and 
attach to the plastic. 

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Egg Heads Puzzle 

• Cut it with a band saw, just outside 
the line, and then sand it down 
exactly to the line. 

• You will trace this 30 times, so be 
sure it's accurate. As a check, you 
can trace it onto paper, then rotate 
it 180° and trace it again. 

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Egg Heads Puzzle 

With a pencil, lay out and trace 30 copies on W-thick wood. Make a couple of extras, too. 
One advantage of using a clear acrylic template is that you can see through it to position it 
where you want, relative to the wood grain, thus avoiding knots. 

For strength, align the template the long way, along (not across) the grain. 

Use a band saw to cut the 30 parts just outside the pencil lines. Then sand to the line. Any 
disk or belt sander is fine for the convex portion at the tops of the heads. A thin belt sander 
with no backing is ideal for the concavities. 

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Egg Heads Puzzle 

• For drilling the eyeholes, first make 
a simple drilling jig that you can 
clamp to your drill press table. A 1" 
square of wood glued to a larger 
scrap of wood is sufficient for the 


• You can hold the notch at the back 
of each egg head against this 
square to position the parts 
consistently under the drill bit. 

• Depending on your woodworking 
tastes, you may round the edges 
slightly, belt-sand the flat surfaces 
to remove any planer marks, 
and/or use an orbital sander with 
progressively finer grits, for a 
sensuous feel. Don't alter the 
geometry of the crucial mating 
points at the backs of the heads 
and the fronts of the necks. 

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Egg Heads Puzzle 

• Use a scroll saw or fine coping saw 
to cut 1 piece along the line 
indicated in the key template. 

• Be sure not to cut the reverse of 
this curve, with the head facing the 
opposite direction. This is the final 
piece in the assembly. 

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Egg Heads Puzzle 

• Apply an appropriate wood finish, 
e.g., tung oil, and allow it to harden. 

• While the above steps are largely 
mechanical for woodworkers, I 
guarantee you'll find the assembly 
step to be a new intellectual 

• It would be easier if you were an 
octopus. When it's done, the parts 
all interlock without any glue, but 
the whole thing wants to fall apart 
until the final pieces are positioned. 
So this is the true test of dedicated 
nerdiness. I'm sure you'll succeed, 
because you have so much time 
already invested! Or perhaps have 
an Egg Heads party so you have 
lots of hands available to hold 
everything in place. 

• The entire puzzle can be scaled up 
or down, but you must scale every 
dimension, including thickness; for 
example, you might triple the size 
to a diameter of 3' using %"-thick 
wood. Send me a photo if you do! 

• If you'd like to test your puzzle 
prowess, stop reading and try to 
assemble your Egg Heads based 
only on the final assembled image. 
If that fails, follow the step-by-step 
assembly instructions and photos 
in the next steps. 

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Egg Heads Puzzle 

First observe how 3 back-of-the- 
head notches can meet and "mind 
meld" like the corner of a cube, 
with all 3 heads facing either 
clockwise or counterclockwise. 

You can assemble the puzzle in 
either of 2 mirror-image solutions, 
but all mind melds must be the 
same. After finishing, you can 
disassemble it and try the other 
handedness. (For the other set of 
instructions, just look at these 
pictures in a mirror.) 

Use 5 twist ties to hold together 1 
pentagon cycle. 

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Egg Heads Puzzle 

Step 10 

• Make another pentagon interlocked 
with the first. 

Step 11 

• Position the 2 pentagons so that 2 
heads of one do a mind meld with 2 
heads of the other. At the opposite 
end of the pentagons, you can do 
the same thing. 

• A rubber band around the mouths 
can keep the heads together. 

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Egg Heads Puzzle 

Step 12 

• Continue adding parts, one at a 
time, making twist-tied neck 
pentagons and rubber-banded mind 
melds. The final few parts have to 
be carefully steered into position, 
but no force is needed. 

• The very last part goes in as 2 
halves, one from each side, and 
locks together. 


The mathematics underlying this puzzle is described in my paper for Joe Malkevitch's 
Festschrift: George W. Hart, "Egg Heads: A Puzzle/Sculpture" in Geometry, Games, Graphs, 
and Education: The Joe Malkevitch Festschrift, ed. Sol Garfunkel and Rishi Nath, Consortium for 
Mathematics and Its Applications (COMAP), 2008. 

This project first appeared in MAKE Volume 17 . page 143. 

This document was last generated on 201 2-1 1 -02 1 2:39:52 AM. 

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